The Gravity Drained Tanks Control Loop

Measurement, computation and control action repeat every loop

sample time: a sensor measures the liquid level in the lower tank this measurement is subtracted from the set point level todetermine a control error; e(t) = ysetpoint y(t) the controller computes an output based on this error and it istransmitted to the valve, causing it to move this causes the liquid flow rate into the top tank to change, whichultimately changes the level in the lower tank

Real processes are nonlinear, so their behavior changes as

Thus, a controller should be designed for a specific level of

Collect Process Data at the Design Level

the design value for the measured process variable is where theset point will be set during normal operation

the design values for the important disturbance variables are

their typical or expected levels during normal operation

perform the dynamic test as near practical to the design level of

the measured process variable when the disturbances are quietand near their typical values

Controller Gain, KC, From Correlations

P-Only control has one adjustable or tuning parameter, KC

u(t) = ubias + KC e(t)

KC sets the activity of the controller to changes in error, e(t)

if KC is small, the controller is sluggish If KC is large, the controller is aggressive

To determine KC, use this controller design procedure:

generate dynamic process data at the design level of operation fit a FOPDT dynamic model to this data use the FOPDT model parameters in a correlation to computeinitial estimates of KC

Copyright 2002Douglas J. CooperAll Rights Reserved

Controller Gain, KC, From Correlations

Integral of time-weighted absolute error (ITAE) tuning correlations:

if set point tracking (servo control) is the objective:

KC

Kp

( p / p ) -1.219

if disturbance rejection (regulatory control) is the objective:

KC

Copyright 2002Douglas J. CooperAll Rights Reserved

0.202

0.490Kp

( p / p ) -1.084

Controller Gain, KC, From Correlations

Copyright 2002Douglas J. CooperAll Rights Reserved

Correlations provide an initial guess or starting point only

Final tuning requires online trial and error because:

the designer may desire performance different from thatprovided by the correlation the FOPDT model used for tuning may not match the actualdynamic behavior of the plant performance must be balanced over a range of nonlinearoperation performance must be balanced for set point tracking anddisturbance rejection

Notes: the designer defines best control performance it is conservative to start with a small KC value

Understanding Controller Bias, ubias

Thought Experiment: Consider P-Only cruise control where u(t) is the flow of gas

Suppose velocity set point = measured velocity = 70 kph

Since y(t) = ysetpoint then e(t) = 0 and P-Only controller is

u(t) = ubias + 0

If ubias were set to zero, then the flow of gas to the engine would bezero even though the car is going 70 kph

If the car is going 70 kph, there clearly is a baseline flow of gas

This baseline controller output is the bias or null value

Copyright 2002Douglas J. CooperAll Rights Reserved

Understanding Controller Bias, ubias

Copyright 2002Douglas J. CooperAll Rights Reserved

In the thought experiment, the bias is the flow of gas which, in

open loop, causes the car to travel the design velocity of 70 kphwhen the disturbances are at their normal or expected values

In general, ubias is the value of the controller output that, in open

loop, causes the measured process variable to maintain steadystate at the design level of operation when the processdisturbances are at their design or expected values

Controller bias is not normally adjusted once the controller is put

in automatic

Reverse Acting, Direct Acting and Control Action

If KP is positive and the process variable is too high, the controller

decreases the controller output to correct the error=> The controller action is the reverse of the problemWhen KP is positive, the controller is reverse actingWhen KP is negative, the controller is direct acting

Since KC always has the same sign as KP , then

KP and KC positive KP and KC negative

Copyright 2002Douglas J. CooperAll Rights Reserved

reverse actingdirect acting

Reverse Acting, Direct Acting and Control Action

Copyright 2002Douglas J. CooperAll Rights Reserved

Most commercial controllers require you to enter a positive KC

The sign (or action) of the controller is specified by entering the

controller as reverse or direct acting

If the wrong control action is entered, the controller will drive

the valve to full open or closed until the entry is corrected

Offset - The Big Disadvantage of P-Only Control

Copyright 2002Douglas J. CooperAll Rights Reserved

Big advantage of P-Only control:

=> only one tuning parameter so its easy to find best tuning

Big disadvantage:=> the controller permits offset

Offset - The Big Disadvantage of P-Only Control

Offset occurs under P-Only control when the set point and/ordisturbances are at values other than that used as the design levelof operation (that used to determine ubias)u(t) = ubias + KC e(t)

How can the P-Only controller compute a value for u(t) that isdifferent from ubias at steady state?